Warm up… You’ll need to pick up the worksheet up front. Remember how we used the calculator on Friday. Need to graph the vertex along with four other points Your papers are graded just not in the computer yet. At the end of class I will share with you your grade on that assignment.

Solving Quadratic Equation by Graphing Section 10-2

Quadratic Equation y = ax 2 + bx + c ax 2 is the quadratic term. bx is the linear term. c is the constant term. The highest exponent is two; therefore, the degree is two.

l Example f(x)=5x 2 -7x+1 Quadratic term 5x 2 Linear term -7x Constant term 1 Identifying Terms

l Example f(x) = 4x Quadratic term 4x 2 Linear term 0 Constant term -3 Identifying Terms

l Now you try this problem. l f(x) = 5x 2 - 2x + 3 l l quadratic term l linear term l constant term Identifying Terms 5x 2 -2x 3

The number of real solutions is at most two. Quadratic Solutions No solutions One solution Two solutions

Solving Equations When we talk about solving these equations, we want to find the value of x when y = 0. These values, where the graph crosses the x-axis, are called the x-intercepts. These values are also referred to as solutions, zeros, or roots.

Example f(x) = x Identifying Solutions Solutions are -2 and 2.

Now you try this problem. l f(x) = 2x - x 2 Solutions are 0 and 2. Identifying Solutions

The graph of a quadratic equation is a parabola. The roots or zeros are the x- intercepts. The vertex is the maximum or minimum point. All parabolas have an axis of symmetry. Graphing Quadratic Equations

Graph y = x 2 - 4x Roots 0 and 4, Vertex (2, -4), Axis of Symmetry x = 2 Graphing Quadratic Equations

Try this problem y = x 2 - 2x - 8. Vertex (1, 9) Axis of Symmetry x = 1 Roots -2 and 4 Graphing Quadratic Equations

No real roots Solve x 2 + 2x + 3 = 0 by graphing. We notice there are no real roots.

Rational roots when you run into a problem with no real roots you can estimate the roots by stating which two integers the root is.

Solve x 2 – 4x + 2 = 0 Notice this function has no real roots we can say one root is between 0 an 1 and the other root is between 3 and 4.

Page 536 #’s 12 – 34 evens Yes you need to graph each one on your paper Class work…